President Richard Trumka said the AFL-CIO wants some higher-skilled laborers to be exempt from any new program until the jobless rate improves. In February, unemployment in the construction industry was 15.7 percent.

‘‘Until the unemployment rate gets down to a certain level you don’t bring them in,’’ Trumka said in a C-SPAN interview airing this weekend. Those are skilled workers. You can’t just bring people in off the street and pay them, as was proposed, 25 percent of market value.’’

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The AFL-CIO says it will oppose any new visa plan that would decrease wages for US workers. Business representatives say the labor group is demanding wages that are higher than those paid to US workers performing the same jobs.

On Wednesday, Senator Charles Schumer, Democrat of New York, said a bipartisan Senate group of eight lawmakers is ‘‘90 percent’’ done with its draft bill.

President Obama, who has called overhauling immigration the top legislative priority of his second term, said Wednesday that he is confident an immigration bill will pass soon.

‘‘Labor and businesses may not always agree exactly on how to do this, but this is a resolvable issue,’’ the president told Telemundo. Still, wary of undermining talks with Republicans, Obama has taken a back seat in the negotiations. Rather than advocate for specific proposals, he has spoken privately to lawmakers.

The toughest issue will be construction, said Geoff Burr, vice president for Associated Builders and Contractors. The AFL-CIO is demanding that some immigrant construction workers be paid from 40 to 60 percent more than what similarly qualified US workers are paid, Burr said, an assertion the labor group disputes.

Trumka said the AFL-CIO proposed last week that the Senate bill include a requirement that visas be issued across all industries at a rate that won’t hurt US wages or benefits. The dispute is over what methodology should be used to determine these wages and what unemployment rate should trigger additional visas.

Under the AFL-CIO’s proposal, the Labor Department would determine what that level should be. The Chamber wants wages to be set under a four-tiered system based on workers’ experience and skills.

The US Chamber says the characterization that immigrants would be paid below the current market rate is false.

The group of eight senators is finalizing a bill that would allow 11 million illegal immigrants
to achieve full citizenship in 13 years.